In their first face-to-face meeting, the new Iraqi prime minister asked President Obama on Wednesday to send more weapons for Iraq’s armed forces to confront the militants of the Islamic State.

“Our armed forces are in dire need for equipment and for weapons,” said Prime Minister Haider al-Abadi, “mostly because we lost a lot of the equipment and the weapons in our confrontation and our fight against” [the Islamic State].

The two leaders met at the United Nations in New York, where Mr. Obama called on other heads of state to join a U.S.-led coalition fighting the terrorist group.

A senior administration official said the Iraqis are not looking for new weapons but want the U.S. “to move a little faster” on supplying promised military hardware. The U.S. has carried out nearly 200 air strikes against the militants in Iraq since Aug. 8.

The administration official said Iraqi forces are in a “pretty desperate struggle against [the Islamic State]” and that four Iraqi divisions “completely unraveled’ when the militants took Mosul earlier this year.

Since then, the official said, U.S. forces have been working to reconstitute to those forces. The aide said that Mr. Al-Abadi fired two of his top military commanders within the past 48 hours.

“That decision was probably long overdue,” the aide said. “He’s looking for new leadership in the ranks. He’s looking to correct the mistakes of the past.”

Mr. Obama said that although the U.S. has pledged additional military “assistance” to Iraq, Mr. Al-Abadi “understands that in order for Iraq to succeed it’s not just a matter of a military campaign.”

“It’s also the need for political outreach to all factions within the country,” the president said. “I’m confident that he’s the right person to help work with a broad-based coalition of like-minded Iraqis and that they will be successful.”

In his speech to the U.N., Mr. Obama said Iraq had been in danger of being overrun by the militants. The president is counting on the new government in Baghdad to govern more inclusively and build stronger security forces capable of defeating the militants.

Mr. Al-Abadi said that in many areas of Iraq, the security forces “are now turning around the ground” that had been seized by the militants.

“I am very thankful for President Obama that he promised that weapons and supplies would be delivered to Iraq as soon as possible so Iraq can defeat [the Islamic State] and Iraq can overcome this crisis.”

He said to Mr. Obama, ‘I hope to see that these promises will be concretely fulfilled on the ground as soon as possible.”